Wednesday, February 28, 2007

Hayek On Reswitching

"...the amount of waiting involved in a particular investment is not simply proportional to the length of the investment period and the value of the input invested, but is dependent also on the rate of interest. In consequence, when we compare two different investment structures, it will not always be possible even to say, on purely technical grounds, which of them involves the greater amount of waiting. At one set of relative values for the different kinds of input and at one rate of interest, the one structure, and at a different set of values or a different rate of interest, the other structure, will represent the greater amount of waiting, or will be 'longer' in the sense in which this term has commonly been used." -- F. A. Hayek (1941). The Pure Theory of Capital, University of Chicago Press: 144
I know about this quotation from Roger W. Garrison's article "Reflections on Reswitching and Roundaboutness".


Anonymous said...

I don't think Hayek goes far enough in explaining why re-switching is a non-problem. Risk/uncertainty would play a major role in making the choice under the case if reswitching did come up. So reading about re-switching, while theoritical it's not a major issue in the real world.

anonymous Mike

Robert Vienneau said...

No. Risk and uncertainty is a separate issue. As for the "real world", note the last sentence here. Of course, the literature does contain analysis of empirical evidence. (That's another point on which Garrison is mistaken.)

Anonymous said...

I don't have access to those instances so maybe you can pick one and describe them with their calculations.

For a reswitching problem to be a concern to a company several things must come into play.

1) Both production methods must be known. It's easy to say afterword that the company should have bought this machine instead of hiring workers but they didn't know that the machine was out there.

2) That after calculating cash flows for both methods the IRR is close to each other other. A company may decide to use more workers if it figures that it's cash flow will be much greaters.

3) The IRR for the switching point must be greater than a firm's internal cost of capital but less than what they think would be a normal rate of profit. If the switching point is at 2% they aren't even going to think of it because it's going to be way lower than a normal loan and on the other side if the company calculates a 100% IRR on it it needs to double check it's numbers.

anonymous Mike

YouNotSneaky! said...

As for the "real world", note the last sentence here

Actually one should read the entire thread to get the entire spectrum of views as there's a few there which disagree.
As I said before, it's not a "logical inconsistency", it's an argument over the appropriate definition of "capital". Otherwise someone can show me where x does not follow from y, given my assumptions.

h.e. said...

"As I said before, it's not a "logical inconsistency", it's an argument over the appropriate definition of "capital". Otherwise someone can show me where x does not follow from y, given my assumptions."

So you admit that all you are doing is engaging in an exercise in applied mathematics? At some point, economics as a disciple lays claims to talking about economic "reality". At this point in time, practitioners better start worrying about how to measure the variables they are interested in (and whether meaningful measurements even exist) before talking about a bunch of ad hoc relationships that supposedly exist. You can't empirically test a theory when you don't even have a clear idea what you're talking about. The theory itself becomes meaningless.

h.e. said...

Sigh...I'm not sure why I waste my time with this, but I thought I would the following quote and link one more time...

This is certainly not 'measurement without theory'; it is theory without the minimal conceptual clarity required to make that theory worthy of attention. No amount of 'sophisticated' mathematical analysis can turn conceptual confusions into meaningful conclusions. - Ian Steedman

Anonymous said...

But "H.E.",

What do you do when the no-nonsense hardcore measurable variables like physical output do in fact depend crucially on such elusive real-world variables like knowledge in its various embodiments, or preferences?

Those variables may be hard to measure but it is nonsense to claim that one can wish them into irrelevance (that is, conveniently include them in some irrelevant error term) or not existing in reality.

Mind you, I do agree that at the very least one should make sure that the variables one talks about belong in the real world -- as such the use of "aggregate productions functions" for instance is invalid and bound to lead to nonsense in applications.

But I also think that Sraffians delude themselves when they think they are able to stitch up a coherent theory only in terms of hardcore observables.

Avi Cohen is well worth quoting here:

“While it is legitimate to determine exogenously all output parameters, it is not legitimate to allow changes in a subset of total output (the wage bundle) yet hold total output constant.


Once prices vary with changes in distribution, the strong classical conceptions of price as an index of the exogenous difficulty of production is immediately violated. The rate of profits, which previously depended only on exogenously given physical magnitudes of outputs and inputs, now depends on the prices of outputs and inputs, which in turn depend on the rate of profits. This internalization of the measure of inputs to production eliminates the necessity of an inverse relation between the real wage and the rate of profits

In other words, by ignoring how changes in distribution affects output –-and to quantify this dependence you need to introduce the consumer and his elusive behavior-- the Sraffian conclusion of an inverse relation between the rate of profit and the real wage is invalidated.(In the sense of such relation being necessary)

At this point all the usual insults about “illogic” and “conceptual inconsistency” “applied mathematics rather than economics” that Sraffians throw at Marshallian partial equilibrium reasoning can be thrown back at them via the inconsistency elucidated above by Avi Cohen.
Ironically, this criticism of Sraffian models has obvious parallels with the Sraffian criticism of Marshallian models.

So remarks about glass houses and stones are what is appropriate when Sraffians attempt to take any theoretical higher ground against their neoclassical colleagues.


Cohen, Avi J. (1989). “Prices, Capital, and the One-Commodity Model in Neoclassical and Classical Theories” History of Political Economy V.21, N.2:231-251

h.e. said...

"Mind you, I do agree that at the very least one should make sure that the variables one talks about belong in the real world -- as such the use of "aggregate productions functions" for instance is invalid and bound to lead to nonsense in applications."

Note that Radek's assertion is that the issue is the relevent defintion of capital. I don't think that there is a "definition" that justifies either aggregate production functions or the application of "microfoundations" to the aggregate production to derive factor demands. That Radek can reach certain conclusions by assuming an aggregate production function where capital and labor enter as arguments thus seems to me to be an empty exercise in mathematics. I would have been just as happy quoting Franklin Fisher.

I don't share Robert's position that the Sraffian critique negates disaggregate neoclassical theory. I also concede that economic outcomes are likely shaped by factors that can not be measured physically. My compliants are more generally directed at applied economists' utter disregard (and often ignorance) with regards to issues of aggregation. Related to this is the apparently ad hoc way in which they impose structure on models to yield stark predictions and pretend that they are engaged in a "scientific" endeavor.

Robert Vienneau said...

"Tu quoque" is a fallacy. Given the fallacious nature of Alex's comment, I see no need to address his misunderstandings and misrepresentations.

Man-Seop Park has demonstrated that Paul Romer’s characterization of his math is incoherent on other grounds than Steedman gives above. Park’s demonstration is downloadable from the Cambridge Journal of Economics web site. H.E., I think you would like this article.

Anonymous said...

Obviously I did not intend the criticism of the Sraffian models as a defense of any piece of neoclassical theory.

It is hard to see how one could interpret my comments in that manner, since I agreed with the misuse of the aggregate production functions in neoclassical theory, as an example.

I welcome any clarifications regarding my misunderstandings -- they would go a long way towards clarifying the Sraffian position relative to Cohen's criticism too.


YouNotSneaky! said...

So you admit that all you are doing is engaging in an exercise in applied mathematics?
At some point, economics as a disciple lays claims to talking about economic "reality"

Applied logic, certainly.

And I'm willing to play a bit of a devil's advocate here and defend APFs. For one, the results of the Neoclassical Growth model fit Kaldor's stylized facts, that is economic "reality".

Also I think in his post up above Robert is right, though not in a way he thinks. The reason for why mainstream economics is what it is, why it focuses on prices as scarcity indexes and tends to teach that demand curves, even for factors, slope downward is because it jives pretty well with intuition.
The idea that prices in the real world have nothing to do with how much people value goods and only with costs of production (a particular form of LTV) just strikes folks as silly. (Not to mention that I can't even think of how to extend this LTV to topics such as imperfect competition, price discrimination etc.)
In a similar way, the idea that when some factor of production, labor or capital, however defined, becomes more expansive more of it is bought also jives with the intuition. Part of the value of formal economics is that we learn that such a situation *could* happen. But it's still up to the proponents of this would be heresy to present convincing empirical evidence that this is a pervasive phenomenon. Shrugging your shoulders and smuggly saying that essentially, emprical evidence is irrelevant because neoclassical is "logically inconsistent" is not gonna win over many followers. So the UK Cambridge won the CCC. Where's the vast follow up empirical literature that would make this victory stratigically significant?

h.e. said...

The reason for why mainstream economics is what it is, why it focuses on prices as scarcity indexes and tends to teach that demand curves, even for factors, slope downward is because it jives pretty well with intuition.

That intuition, especially when it comes to production, is, I think, largely learned in the classroom. Probably in intermediate microeconomics. At some point in time, you have to address Robinson's quip about economists talking glibbly about a unit of capital without being able to talk about the unit.

So even with a firm's isoquant, what is meant by a unit of capital? If I'm using a (nominal) dollar measure, then I'm working with a measure that won't survive in a G.E. framework, since Wicksell price effects will come into play (leading to a new isoquant for each set of factor prices). If I use a real measure, I end up with a measure that is irrelevant for economic decision making (the rental price of a unit of capital will be a non-linear function of the factor prices). If I'm talking about a single capital good (hopefully not the generic "machine"), then there becomes a question of how the model generalizes (especially in a general equilibrium framework). Although this may be useful as for pedogogical purposes, it abuses the notion of "substitution", which involves different capital goods at different "intensities".

My take is that the problem extends beyond macroeconomics and results in a general "fuzziness" within economics. I think you're wrong; substitution in production is a learned intuition. Of course, even if it was a folk intuition, one of the purposes of formal study is to test whether such folk intuitions are justified. (I never understand why Instrumentalists are so concerned about model intuitions.)

The issue of empirical relevance is a red herring. If interest rates are constant over time, there may simply not be the variation in factor prices necessary to generate substantial Wicksell price effects.

Your references to imperfect competition and the like is a non-sequitor, since both the Solow model and the underlying distributional theory assume perfect competition.

YouNotSneaky! said...

I'll reply in more detail later, but just for starters this

That intuition, especially when it comes to production, is, I think, largely learned in the classroom

is probably way wrong. Rather I think the intuition is there because it corresponds to most folks everyday experience. Personally I didn't take an econ class until grad school (in another discipline). So no econ classroom either as high school student or undergrad. Depending on the university a lot of students never take an econ class (though apparantly the major has been gaining in popularity lately). At the high school level economic education (like pretty much all education) is even worse. Usually taught by some coach who thinks economics is about balancing one's checkbook (this was the econ class at my high school).
I seriously, seriously doubt that the commonplace of the idea that "scarcity drives up price" is a result of neoclassical brainwashing. I mean, you got any proof for that assertion?

h.e. said...

Clearly people do equate high prices of NYC real estate, Playstation 3's at Christmas time, and gasoline at the pump with scarcity. That the interest rate represents the "price" of capital and is related to the relative scarcity of capital, however defined, is a different issue. I don't think this forms part of everyday thought or experience, but is indeed a product of the classroom. (Note my qualifier about production.)

And again, the function of a discipline is not to merely confirm convention wisdom.

Robert Vienneau said...

H. E. may not disagree with everything I say, but I have no disagreement with his last two comments.

Robert Vienneau said...

Should be "may not agree".

YouNotSneaky! said...

he and Robert,

(and one argument at a time)
I don't think that most people think about the relationship between rate of interest and stock of capital very often, wherever they get their ideas from. They do probably think about the relationship between wages and amount of labor highered. And the intuition "at higher wages less labor is hired" is probably either due to their personal labor market experience or is an application of their experience with regular downward sloping demand curves for regular goods. I think blaming this "on the classroom" (especially given how few people go through the classrooms) is pretty silly - vestiges of Marxist accusations of "false conciousness" or something.

Of course personally I have my students chant "Labor demand curve is downward sloping! Always and Everywhere!" all the time while sounds of the ocean play in the background.

h.e. said...

You're making some big leaps here. I agreed that price-scarcity relationship relationships may be familiar from everyday experience. However, you have yet to address the issue, which is of substitution as a learned intuition. Presumably a role of microeconomic theory is to explain why scarcity leads to higher prices. From the perspective of consumer goods, the early neoclassical solution was to assume diminishing marginal utility, which was later relaxed to diminishing marginal rate of substitution. From an analytic perspective, there are problems with extending this idea of substitutibility to production, particularly when talking about capital as an input.

YouNotSneaky! said...

From an analytic perspective...

Yes, I know there's problems from the analytic perspective, obviously. But I was questioning the assertion that these ideas are "brainwashed" into people by their economics classes. I think most people take their everyday experience with goods and intuition and apply it to factor, specifically labor, markets.

And come on, even in Sraffian models the negative relationship between price and quantity holds if you're far away from the switch points, if these exist at all.

Anyway, the reason why I'm not willing to throw APFs out the window (this is addressing the other issue raised) is that I think there's a good bit of research that uses them that has interesting things to say. For example, it's much easier to introduce imperfect competition, political economy considerations, directed technological growth, endogenous population growth and human capital accumulation and many other problems of interests in a APF framework. I think folks like Oded Galor or Daron Acemoglu have many interesting things to say, even though their models use APF. The linear production models are essentially so focused on capital as a factor of production that it's hard for them ponies to do any tricks other than generate Wicksell effects.

h.e. said...


I don't believe that I've ever used the word "brainwashed". But let me make an argument that you may find acceptable: students readily accept supply and demand analysis because it is an appealing idea, at least superficially. I think the dominance of neoclassical theory does depend in part on its appeal, rather than some widespread conspiracy by the powers that be. I'm more skeptical about the acceptance being related to a correspondance with everyday experiences; most freshmen don't seem to have a lot of experience with labour markets for example.

I think that Robert has a valid point though; most students are never exposed to any other approaches. So students that buy into supply and demand self-select into economics and students that don't opt to major in other subjects. And so economics ends up being defined by a methodology rather than by the domain of study.

I'm aware that you are familar with the Sraffian critique. I wasn't until after I finished grad school. What still amazes me is how upset other economists get when I mention it.

There may be a place for APFs in research. However, economists should also be aware of the controversies surrounding their use, which to me means that both the Sraffian critiques and issues of aggregation should form a part of undergraduate instruction (not necessarily at a technical level). Even if your comment about switch points defends supply and demand analysis for specific goods, it doesn't defend this practice for poorly defined categories of goods (e.g. "capital").

YouNotSneaky! said...


Alright, I generally, tentatively agree.As far as teaching the controversies and critiques at the undergrad level, I think this is difficult. Aside from some general comments about aggregation etc. it's hard to explain this stuff without technical examples.But you're right, I think there should be more of it.